In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5 \,{mm}$ on a complete rotation. For a particular observation the reading on the main scale is $5\, {mm}$ and the $20^{\text {th }}$ division of the circular scale coincides with reference line. Calculate the true reading. (in ${mm}$)
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The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as
Diameter of a steel ball is measured using a Vernier callipers which has divisions of $0. 1\ cm$ on its main scale $(MS)$ and $10$ divisions of its vernier scale $(VS)$ match $9$ divisions on the main scale. Three such measurements for a ball are given as
S.No.
$MS\ (cm)$
$VS$ divisions
$(1)$
$0.5$
$8$
$(2)$
$0.5$
$4$
$(3)$
$0.5$
$6$
If the zero error is $- 0.03\ cm,$ then mean corrected diameter is $........... cm$
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
In an experiment on simple pendulum to determine the acceleration due to gravity, a student measures the length of the thread as $63.2 \,cm$ and diameter of the pendulum bob as $2.256 \,cm$. The student should take the length of the pendulum to be ........... $cm$